The GoI is basically the Foundation + anomalous tech. Which is to say that it's basically the Chaos Insurgency and/or the Global Occult Coalition. It's not particularly interesting beyond that.

The way that new groups of interest get added is by having several successful tales/SCP articles that involve them, not by randomly adding stuff to the GoI page and hoping that if you build it, they will come.

"FitzsStrike" is, frankly, a dumb sounding name that combines Norman French and Anglo-Saxon roots nonsensically. "Fitz" is Norman French for "son of", and "strike", of course, is a modern English verb meaning "to hit" and comes from the Anglo-Saxon verb striecen. I'm sorry, but the "Son of Hit Team" just sounds stupid.

That capsule writeup doesn't really interest me or make me care about the group either.

The second tab reads like an action story told by a child. The radio talk is just wrong, and feels like it was gleaned from movies. The "communicator" thing instead of "radio" reminds me of the creative writing class in Throw Mama from The Train where one of the stories is about a submarine but the author obviously didn't do any research. "Egyptian" is a dead language, any village where they speak it is completely weird in and of itself and should probably be at least lampshaded, unless you actually meant Arabic in which case, again you didn't do the research (not even bothering to read the summary on the country's wikipedia page). The whole thing with the commander and some soldier not being named characters but this "Charlie" is, is just weird. Also real world operators don't usually use first names. The whole thing has a very difficult to define quality beyond these problems that I dislike, maybe it is the lack of sophistication in the writing? It reminds me of bad military fiction.

The SCP object is uninteresting, merely a piece of technology, and probably shouldn't even be an SCP object. It seems like a comic book weapon. Much of the article seems to be there to make it sound cool. It doesn't. The test with the deer doesn't make much sense. Why a deer and not like a lab rat or a pig, or really just ballistic gel? Why would an electric shock propel its head off? Why do we care if the D-Class is squeamish?

1. Each of the members of the FitzStrike Team, their last names are Fitzgerald.
2. If operators don't use names, what do they use?
3. It's not an SCP, it's an SCP dash F. Those are objects recovered from the FitzStrike Team.

It still sounds stupid. It also is stupid to include a clue to your real names in the name of your group. Also a Foundation-scale covert occult organization that only recruits Geraldine Norman-Irish people, is just plain silly.

Last names ("Jenkins") , or on sanitized operations, callsigns ("Pretty Boy") or rank ("Corporal") or grade and last initial ("EchoFourJuliet").

1. There's enough Fitzgerald brothers to staff an entire organization large enough to rival the Foundation? That Gerald sure had a lot of kids… .
3. That doesn't actually change anything. It still is a silly comic book weapon, not interesting, with nonsense testing.

Why have them named "FitzStrike" then? Again, it's stupid to clue their real name in because communcations can be hacked and put them or their family at risk. Also, we're expected that, at most, three to six brothers give the Foundation (a worldwide secret organization that can effectively keep reality-destroying monsters hidden and safe from the public) continual headaches and are able to slip away without any kind of apparant support network?

Communications can be hacked, but they terminate a channel as soon as hacking is detected.
They have no other family, and their support comes from autonomous robotic assistants that they have built themselves. They are their own support.
We don't always slip away, sometimes the Foundation has attacked us.
The base is mobile, so worldwide structures are obsolete.

1. As if you could detect a hack quickly enough not to be compromised. My fictional hacker is as badass as your fictional strike team.

2. No one is their own support. Let's assume, for the moment, that they grow their own food, sanitize their own water, produce their own power. If someone neutralizes the farm, you've got to connect to the world market. And that only works if you're offering services to the world market in return. Which, if they're their own support, they aren't.

3. Once again, if you're self-supporting, you've got your own farm and power plant. Those are much, much more expensive if they're mobile.

There's also plumbing, unless there's a trail of unwashed clothes and feces these people leave behind wherever they go on missions. Being self-supporting in all terrains following the Foundation would be crazy hard.

Something something After Hours alternate universe episode Twilight Zone poop in a new house every day

To clarify, this is the Cracked youtube After Hours series, and I forget which episode it actually is where Dan says if he lives in the Twilight Zone verse his survival would involve pooping a different house every day

I'm going to be as direct as I can here, because there seems to be an overall lack of understanding on your part.

This concept is terrible. It is a juvenile action movie pastiche with no redeeming qualities, and is obviously an attempt to force a new GoI without doing the work associated with it, namely writing something of actual entertainment value. All of the people commenting above have been correct in their criticism; you need to focus on listening to that rather than engaging in these endless "but no it's this" exchanges. This idea is not workable in anything close to its current form.

I would line-by-line what you've written, because it's very inexpertly executed and contains numerous basic errors, however I'm not going to invest the time in such an enterprise until you've demonstrated at least some awareness of how we conduct ourselves here. I would advise that you spend some more time reading extant articles, especially more recent ones, to get a feel for what successful writing looks like. I would also advise that you pay attention to how the critique process works here.

This idea is bad. There is no tinkering around the edges or slight changes that can be made to it that will make it into something good. It's not a few revisions away from being fit for consumption, nor is there any indication that it's the start of something that could eventually be up to site standards. It is fundamentally awful.

Going to echo pretty much everything everyone said above.
If you want it to work, you're going to have to demolish this concept and rebuild it from the ground up as something that isn't "the Foundation but better you guiz". And even with the flimsy justification for a name, you need to change it. It really, really, really sounds incredibly stupid, and most of the people reading a hypothetical background on them are going to (perhaps not inaccurately) write it off as some arbitrarily-badass-just-to-be-badass OC GoI without any real raison d'etre.
TLDR: The GOI is entirely pointless, with the core of its concept being done, much better, by already-extant GOIs, and a lot of stuff that make it unique are materials that are of questionable value, and should probably be removed.

Though now I want to write a skip about how Gerald Fitzgerald, the 15th Earl of Desmond has been alive and well in Tir Na Og, building an army from his loins since 1583 and is finally ready to kick off the 3rd Desmond Rebellion and drive the English out of Ireland for good…